In a saucepan over medium heat, combine the cherries, sugar, and orange juice. Bring it to a simmer. In a small bowl, stir together the cornstarch with 2 tablespoons water to make a slurry. Stir the slurry into the cherry mixture and simmer until it thickens, about 2 minutes.
Remove from the heat and let cool.
In parfait glasses, put a small scoop of ice cream, a spoonful or 2 of the cherry mixture, and some of the cookie pieces. Repeat 2 to 3 times to fill up the glass.
